Best ways to use sauna and steam?

I just joined a gym that has a sauna room and a steam room. I heard there are great benefits to both. I never really used them except the sauna to cut water weight.

I work out at 6 am in the morning for about one hour and got class at 7:30.

If I am on time constraint, which one would be better to do, and for how long? Is there any special type of programs you do for either of them, like mixing them, or working out in them, or whatever?

I am used to drinking a protien shake right after my workouts, but how do I do that if I go use the sauna? Should I wait until after the sauna, or before? Also, finally, I normally do not really do a cool down after my workouts since I just jog to my car and that normally works for me. Do I have to do a cool down before going to the sauna?